Question

find one counterexample to show that the conjecture is false. ∠1 and ∠2 are supplementary, so one of the angles is acute. choose the best counterexample for the conjecture. a. m∠1=103° and m∠2=77° b. m∠1=38° and m∠2=52° c. m∠1=34° and m∠2=150° d. m∠1=90° and m∠2=90°

Explanation:

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\). An acute angle is less than \(90^\circ\), a right angle is \(90^\circ\), and an obtuse angle is greater than \(90^\circ\) but less than \(180^\circ\).

Step2: Analyze each option

• Option A: \(103^\circ + 77^\circ = 180^\circ\). \(77^\circ\) is acute, so this doesn't counter the conjecture.
• Option B: \(38^\circ + 52^\circ = 90^\circ\), not supplementary. Eliminate.
• Option C: \(34^\circ + 150^\circ = 184^\circ\), not supplementary. Eliminate.
• Option D: \(90^\circ + 90^\circ = 180^\circ\). Both angles are right (not acute), so this shows the conjecture is false.

Answer:

D. \( m\angle1 = 90^\circ \) and \( m\angle2 = 90^\circ \)